BDL26 Random Seed Embedding: seed region card

Proved

QEC.Coding.BDL26RandomSeedEmbedding.seed_region_card

by marwahaha · Nov 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-qecert-4a64933quantum-computingquantum-error-correction

The very same full-H subsystem region is a subset of all five physical labels.

Source: https://github.com/QudeLeap/Lean-QECert/blob/4a64933303628b4f94c4567347e86636853f64a4/QEC/Coding/FiniteAlternatingConstruction/RandomPerturbation/SeedEmbedding.lean#L130-L132

Preamble

import Definitions.Def_QEC_Coding_FiniteAlternatingConstruction_RandomPerturbation_PhysicalLocality
import Definitions.Def_QEC_Coding_FiniteAlternatingConstruction_RandomPerturbation_RandomizedEmbeddingStep
import Definitions.Def_QEC_Coding_FiniteAlternatingConstruction_RandomPerturbation_SeedEmbedding
set_option autoImplicit false
noncomputable section
open QEC QEC.Coding QEC.Coding.BDL26RandomSeedEmbedding
open Classical BDL26FiniteTannerSquare BDL26DecodingGraph BDL26ReplacementEmbedding
open BDL26RandomPerturbation BDL26RandomPhysicalLocality BDL26CSSHamiltonian
open Semantics Semantics.Davies
open QEC.Coding.ProbabilisticConstruction.SphericalCap

Formal statement

theorem QEC.Coding.BDL26RandomSeedEmbedding.seed_region_card (S : OddScale) (q : Physical S 0) : (region S 0 q).card ≤ 5 := by sorry

Source

https://github.com/QudeLeap/Lean-QECert/blob/4a64933303628b4f94c4567347e86636853f64a4/QEC/Coding/FiniteAlternatingConstruction/RandomPerturbation/SeedEmbedding.lean#L130-L132

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